1. Field of the Invention
This invention relates to apparatus and a method for calibrating an on-line predictor of the performance of the core of a nuclear reactor and more particularly to such a method and apparatus for periodically updating axially dependent transverse buckling factors used in a one dimensional neutron diffusion theory model of the core of a pressurized water reactor (PWR).
2. Prior Art
A number of attempts have been made by various groups over the past two or three decades to develop a reactor core response predictor that would serve as an aid to nuclear plant operators in various operations involving change of state of the reactor core. Typical applications of such a predictor would include: assessing the core shutdown margin when the reactor is subcritical, estimating at what point in a startup operation criticality would occur, identifying the most rapid or least water consuming route to follow in a power increase or other maneuver, determining the maximum power level attainable (i.e., the maximum spinning reserve obtainable) when the plant is at a reduced power level, evaluating the closeness of approach to an operating limit during a maneuver, and so on.
In order to simplify the calculations that would have to be done if a practical core response predictor were to be used, the three dimensional, multi-energy group, diffusion theory model of a typical PWR core has been modified to a one dimensional (axial), two energy group diffusion theory representation, for which the computational resource requirements fall within the capability of typical on-site plant digital computers. In the process of reducing the three dimensional core model to a one dimensional model, account had to be taken of the flow in the x-y, or transverse, sense of neutrons from regions of high multiplication potential to regions of lower multiplication potential, and ultimately from the core to the surrounding media. According to the basic precepts of neutron diffusion theory, this transverse flow of neutrons can be accounted for by the inclusion of a transverse buckling term in the overall neutron balance equations, and this has been the standard practice for a number of years by specialists in PWR core design in predicting reactor core responses.
A significant source of error that exists when a simplified one dimensional diffusion theory model is used in lieu of the more nearly valid three dimensional model lies in the choice of the value of the transverse buckling term to be incorporated into the one dimensional model. It has been common practice to use a single value for the transverse buckling at all core elevations in the one dimensional axial model. For PWR cores characterized by high uniformity in nuclear properties in the axial direction, this approach is acceptable. However, for those PWR cores that shows significant variation in nuclear properties at different axial elevations, as a result either of core depletion due to prolonged operation at power or optimized fuel loading designs that seek to improve the commercial aspects of the core loading, the use of a single transverse buckling value that is constant over core height leads to unacceptable errors in the calculated values of both core reactivity and core axial power distribution.
Additional difficulties arise if the initial conditions, especially the core average axial distributions of iodine-135, xenon-135 and local fuel burnup, supplied to the predictor do not faithfully reproduce actual core conditions when the predictor is initialized. Accurate reproduction of the xenon-135 axial distribution is particularly important since the xenon-135 nucleus has a very high cross-section for neutron absorption and so strongly affects both core reactivity and core power distribution. The xenon-135 has a half life of several hours and most of it is not produced directly from fission of the uranium fuel, but through decay of an intermediate fission product, iodine-135. The distribution of power throughout the core depends upon the distribution of xenon, which in turn, depends upon the recent distribution of power. Thus, the response of a core to proposed changes in operating conditions is a function not only of its present condition, but also its recent past.
Diffusion theory equations have been developed and used for many years to analyze core performance. They are three-dimensional, multi-energy group, partial differential equations which characterize the movement of neutrons throughout the core. Such equations are time consuming to set up and require a great deal of computer capacity and time to solve. Hence, this approach is used mainly, and only to a limited degree, for analysis during the design phase and when sufficient lead time is available to set up and solve the three dimesional equations.
For some time, two of the present inventors have used a one dimensional diffusion theory model of a reactor core with transverse buckling factors which are a function of core height. While this model uses axial offset, which is a well known characterization of power which can be in determining the coefficients for the functions selected for the particular buckling factor distribution employed, it also requires the use of the second derivative of the flux distribution at the top and bottom nodes of the core. These data cannot be measured with the necessary accuracy by practical means. Hence, this model is useful in making analytical predictions, such as those made during the design phase, but it is not suitable for an on-line predictor which should be calibrated periodically using operating plant data in order to generate meaningful predictions.
In fact, presently available core predictors have proven to be not satisfactory, due in large part to failure to provide a convenient method for adjusting the core model used by the predictor to adequately reflect actual core characteristics as core depletion progresses. It is recognized that in some more recent attempts, such as an ongoing Electric Power Research Institute (EPRI) sponsored program, to develop usable and effective predictors, reasonable and apparently acceptable degrees of success have been reported when a three dimensional, multigroup, nodal computation scheme has been used in connection with signals from an array of fixed incore neutron or gamma ray detectors permanently installed in the core. Unfortunately, the costs of both the computer and the incore instrumentation required to support this approach tend to be undesirably high. In addition, such three dimensional models are not suitable for predictors used in plant protection or control systems, due to the length of time required to generate a prediction.
Japanese Patent Publication No. 1979-39795, published on Mar. 27, 1979 suggests an on-line predictor for a boiling water reactor (BWR) based upon a one dimensional diffusion model which utilizes incore neutron detectors. It appears that realistic initial conditions are generated by periodically calculating the xenon distribution. It also appears that height dependent radial buckling factors are determined analytically by rearranging the simplified diffusion equation, and that these buckling factors are adjusted analytically for changes in moderator density from initial conditions. However, there is no indication that the buckling factors are adjusted to agree with actual conditions. In other words, there is no indication that the one dimensional model used is ever calibrated using operating plant data to bring it closer to the actual state of the reactor core.
U.S. Pat. No. 4,299,657 suggests a simplified diffusion model for an on-line core predictor, however, there is no indication at all as to what this model is. This patent also suggests that some parameters calculated by the predictor can also be measured, and that periodically the calculated values should be replaced by the measured values. This would suggest periodic reintialization of the calculations, but there is no suggestion that it would be desirable to, let alone as to how to, calibrate the model to adjust it to changing conditions in the core.
It is a primary object of the present invention to provide a reactor core predictor which provides accurate real time predictions of core performance.
It is another object of the invention to achieve the primary object utilizing a one dimensional, few group diffusion theory model.
It is yet another object of the invention to satisfy the above objects by providing a method and apparatus for periodically calibrating the one dimensional diffusion theory model to adjust the model to represent more closely the actual condition of the reactor core.
It is still another object to achieve this latter object by utilizing height dependent transverse buckling factors which can be reliably adjusted through use of measured parameters.